Question

THE AREA OF A CIRCLE IS EQUAL TO THE SUM OF THE AREA OF TWO CIRCLE OF DIAMETERS 10CM AND 24CM , FIND THE DIAMETER AND CIRCUMFERENCE OF THE LALARGE CIRCLE

Answer 1

Step-by-step explanation:

Radius of the first circle r_1=\dfrac{10}{2}=5r

1

=

2

10

=5 cm

Radius of the second circle r_2=\dfrac{24}{2}=12r

2

=

2

24

=12 cm

\therefore∴ Sum of their area = \pi {r_1}^2+\pi {r_2}^2πr

1

2

+πr

2

2

\Rightarrow \pi 5^2+\pi 12^2⇒π5

2

+π12

2

\Rightarrow 25\pi+144\pi = 169\pi⇒25π+144π=169π

Let the radius of the larger circle be r

\therefore Area=\pi r^2∴Area=πr

2

According to the question -

\Rightarrow \pi r^2=169 \pi⇒πr

2

=169π

\Rightarrow r^2=169⇒r

2

=169

\Rightarrow r=\sqrt{169}=13⇒r=

169

=13 cm

radius of circle is 13cm

diameter of circle is 2\ times 13 = 26cm